where \(\lbrace |i_A \rangle \rbrace _{i=0}^{n-1}\)  and \(\lbrace |i_B \rangle \rbrace _{i=0}^{n-1}\)  are orthonormal basis of the two subsystems, and \(\lambda (|\psi \rangle )=(\lambda _0^2, \lambda _1^2, \cdots , \lambda _{n-1}^2)^T\) .
The entanglement monotone \(E_f\)  can be extended to mixed states by the convex roof construction [1]}, [2]}. The entanglement of convex roof \(E_{c}\)  is given by
\(E_{c}(\rho )=\min \sum _k p_k {E_f}(|\psi _k\rangle ),\) 
